Properties

Label 525.2.j.b.218.10
Level 525
Weight 2
Character 525.218
Analytic conductor 4.192
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 218.10
Character \(\chi\) \(=\) 525.218
Dual form 525.2.j.b.407.10

$q$-expansion

\(f(q)\) \(=\) \(q+(1.24414 + 1.24414i) q^{2} +(-1.66575 - 0.474620i) q^{3} +1.09578i q^{4} +(-1.48194 - 2.66293i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(1.12498 - 1.12498i) q^{8} +(2.54947 + 1.58120i) q^{9} +O(q^{10})\) \(q+(1.24414 + 1.24414i) q^{2} +(-1.66575 - 0.474620i) q^{3} +1.09578i q^{4} +(-1.48194 - 2.66293i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(1.12498 - 1.12498i) q^{8} +(2.54947 + 1.58120i) q^{9} -1.55221i q^{11} +(0.520079 - 1.82530i) q^{12} +(4.50889 + 4.50889i) q^{13} -1.75948 q^{14} +4.99083 q^{16} +(2.13370 + 2.13370i) q^{17} +(1.20467 + 5.13914i) q^{18} +4.20993i q^{19} +(1.51347 - 0.842259i) q^{21} +(1.93117 - 1.93117i) q^{22} +(3.76050 - 3.76050i) q^{23} +(-2.40787 + 1.34000i) q^{24} +11.2194i q^{26} +(-3.49632 - 3.84392i) q^{27} +(-0.774834 - 0.774834i) q^{28} +2.97115 q^{29} -5.79770 q^{31} +(3.95934 + 3.95934i) q^{32} +(-0.736708 + 2.58559i) q^{33} +5.30926i q^{34} +(-1.73265 + 2.79366i) q^{36} +(1.23123 - 1.23123i) q^{37} +(-5.23775 + 5.23775i) q^{38} +(-5.37069 - 9.65070i) q^{39} -2.68458i q^{41} +(2.93087 + 0.835085i) q^{42} +(2.09578 + 2.09578i) q^{43} +1.70088 q^{44} +9.35721 q^{46} +(0.0358428 + 0.0358428i) q^{47} +(-8.31349 - 2.36874i) q^{48} -1.00000i q^{49} +(-2.54153 - 4.56692i) q^{51} +(-4.94075 + 4.94075i) q^{52} +(-4.30833 + 4.30833i) q^{53} +(0.432457 - 9.13231i) q^{54} +1.59096i q^{56} +(1.99811 - 7.01270i) q^{57} +(3.69653 + 3.69653i) q^{58} -4.93760 q^{59} +3.31687 q^{61} +(-7.21316 - 7.21316i) q^{62} +(-2.92083 + 0.684672i) q^{63} -0.129684i q^{64} +(-4.13342 + 2.30028i) q^{66} +(-1.71008 + 1.71008i) q^{67} +(-2.33807 + 2.33807i) q^{68} +(-8.04889 + 4.47927i) q^{69} -5.73577i q^{71} +(4.64692 - 1.08929i) q^{72} +(-7.26776 - 7.26776i) q^{73} +3.06366 q^{74} -4.61315 q^{76} +(1.09758 + 1.09758i) q^{77} +(5.32495 - 18.6887i) q^{78} +3.59379i q^{79} +(3.99962 + 8.06245i) q^{81} +(3.34000 - 3.34000i) q^{82} +(12.2139 - 12.2139i) q^{83} +(0.922931 + 1.65843i) q^{84} +5.21490i q^{86} +(-4.94920 - 1.41016i) q^{87} +(-1.74620 - 1.74620i) q^{88} -1.35643 q^{89} -6.37653 q^{91} +(4.12069 + 4.12069i) q^{92} +(9.65754 + 2.75170i) q^{93} +0.0891871i q^{94} +(-4.71611 - 8.47447i) q^{96} +(-10.9812 + 10.9812i) q^{97} +(1.24414 - 1.24414i) q^{98} +(2.45435 - 3.95731i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 4q^{3} + O(q^{10}) \) \( 24q + 4q^{3} - 16q^{12} + 8q^{13} - 16q^{16} + 20q^{18} + 4q^{21} - 8q^{22} + 16q^{27} - 28q^{33} + 16q^{36} + 16q^{37} + 20q^{42} + 40q^{43} - 64q^{46} - 16q^{48} - 20q^{51} - 4q^{57} - 40q^{58} + 32q^{61} + 8q^{63} - 16q^{66} - 24q^{67} + 8q^{72} - 32q^{73} + 32q^{76} - 60q^{78} + 52q^{81} + 80q^{82} - 4q^{87} - 96q^{88} - 24q^{91} + 76q^{93} - 96q^{96} - 24q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.24414 + 1.24414i 0.879741 + 0.879741i 0.993508 0.113766i \(-0.0362914\pi\)
−0.113766 + 0.993508i \(0.536291\pi\)
\(3\) −1.66575 0.474620i −0.961723 0.274022i
\(4\) 1.09578i 0.547890i
\(5\) 0 0
\(6\) −1.48194 2.66293i −0.605000 1.08714i
\(7\) −0.707107 + 0.707107i −0.267261 + 0.267261i
\(8\) 1.12498 1.12498i 0.397740 0.397740i
\(9\) 2.54947 + 1.58120i 0.849824 + 0.527067i
\(10\) 0 0
\(11\) 1.55221i 0.468008i −0.972236 0.234004i \(-0.924817\pi\)
0.972236 0.234004i \(-0.0751828\pi\)
\(12\) 0.520079 1.82530i 0.150134 0.526919i
\(13\) 4.50889 + 4.50889i 1.25054 + 1.25054i 0.955478 + 0.295062i \(0.0953402\pi\)
0.295062 + 0.955478i \(0.404660\pi\)
\(14\) −1.75948 −0.470242
\(15\) 0 0
\(16\) 4.99083 1.24771
\(17\) 2.13370 + 2.13370i 0.517499 + 0.517499i 0.916814 0.399315i \(-0.130752\pi\)
−0.399315 + 0.916814i \(0.630752\pi\)
\(18\) 1.20467 + 5.13914i 0.283943 + 1.21131i
\(19\) 4.20993i 0.965823i 0.875669 + 0.482912i \(0.160421\pi\)
−0.875669 + 0.482912i \(0.839579\pi\)
\(20\) 0 0
\(21\) 1.51347 0.842259i 0.330267 0.183796i
\(22\) 1.93117 1.93117i 0.411726 0.411726i
\(23\) 3.76050 3.76050i 0.784119 0.784119i −0.196404 0.980523i \(-0.562926\pi\)
0.980523 + 0.196404i \(0.0629263\pi\)
\(24\) −2.40787 + 1.34000i −0.491505 + 0.273526i
\(25\) 0 0
\(26\) 11.2194i 2.20030i
\(27\) −3.49632 3.84392i −0.672868 0.739763i
\(28\) −0.774834 0.774834i −0.146430 0.146430i
\(29\) 2.97115 0.551728 0.275864 0.961197i \(-0.411036\pi\)
0.275864 + 0.961197i \(0.411036\pi\)
\(30\) 0 0
\(31\) −5.79770 −1.04130 −0.520649 0.853771i \(-0.674310\pi\)
−0.520649 + 0.853771i \(0.674310\pi\)
\(32\) 3.95934 + 3.95934i 0.699919 + 0.699919i
\(33\) −0.736708 + 2.58559i −0.128244 + 0.450094i
\(34\) 5.30926i 0.910531i
\(35\) 0 0
\(36\) −1.73265 + 2.79366i −0.288775 + 0.465610i
\(37\) 1.23123 1.23123i 0.202414 0.202414i −0.598620 0.801033i \(-0.704284\pi\)
0.801033 + 0.598620i \(0.204284\pi\)
\(38\) −5.23775 + 5.23775i −0.849675 + 0.849675i
\(39\) −5.37069 9.65070i −0.859998 1.54535i
\(40\) 0 0
\(41\) 2.68458i 0.419261i −0.977781 0.209631i \(-0.932774\pi\)
0.977781 0.209631i \(-0.0672261\pi\)
\(42\) 2.93087 + 0.835085i 0.452242 + 0.128856i
\(43\) 2.09578 + 2.09578i 0.319603 + 0.319603i 0.848615 0.529011i \(-0.177437\pi\)
−0.529011 + 0.848615i \(0.677437\pi\)
\(44\) 1.70088 0.256417
\(45\) 0 0
\(46\) 9.35721 1.37964
\(47\) 0.0358428 + 0.0358428i 0.00522821 + 0.00522821i 0.709716 0.704488i \(-0.248823\pi\)
−0.704488 + 0.709716i \(0.748823\pi\)
\(48\) −8.31349 2.36874i −1.19995 0.341899i
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) −2.54153 4.56692i −0.355885 0.639497i
\(52\) −4.94075 + 4.94075i −0.685158 + 0.685158i
\(53\) −4.30833 + 4.30833i −0.591794 + 0.591794i −0.938116 0.346322i \(-0.887431\pi\)
0.346322 + 0.938116i \(0.387431\pi\)
\(54\) 0.432457 9.13231i 0.0588500 1.24275i
\(55\) 0 0
\(56\) 1.59096i 0.212601i
\(57\) 1.99811 7.01270i 0.264657 0.928855i
\(58\) 3.69653 + 3.69653i 0.485378 + 0.485378i
\(59\) −4.93760 −0.642821 −0.321410 0.946940i \(-0.604157\pi\)
−0.321410 + 0.946940i \(0.604157\pi\)
\(60\) 0 0
\(61\) 3.31687 0.424681 0.212341 0.977196i \(-0.431891\pi\)
0.212341 + 0.977196i \(0.431891\pi\)
\(62\) −7.21316 7.21316i −0.916073 0.916073i
\(63\) −2.92083 + 0.684672i −0.367989 + 0.0862606i
\(64\) 0.129684i 0.0162105i
\(65\) 0 0
\(66\) −4.13342 + 2.30028i −0.508788 + 0.283145i
\(67\) −1.71008 + 1.71008i −0.208919 + 0.208919i −0.803808 0.594889i \(-0.797196\pi\)
0.594889 + 0.803808i \(0.297196\pi\)
\(68\) −2.33807 + 2.33807i −0.283533 + 0.283533i
\(69\) −8.04889 + 4.47927i −0.968972 + 0.539240i
\(70\) 0 0
\(71\) 5.73577i 0.680711i −0.940297 0.340356i \(-0.889453\pi\)
0.940297 0.340356i \(-0.110547\pi\)
\(72\) 4.64692 1.08929i 0.547644 0.128374i
\(73\) −7.26776 7.26776i −0.850627 0.850627i 0.139583 0.990210i \(-0.455424\pi\)
−0.990210 + 0.139583i \(0.955424\pi\)
\(74\) 3.06366 0.356143
\(75\) 0 0
\(76\) −4.61315 −0.529165
\(77\) 1.09758 + 1.09758i 0.125080 + 0.125080i
\(78\) 5.32495 18.6887i 0.602931 2.11608i
\(79\) 3.59379i 0.404333i 0.979351 + 0.202166i \(0.0647982\pi\)
−0.979351 + 0.202166i \(0.935202\pi\)
\(80\) 0 0
\(81\) 3.99962 + 8.06245i 0.444402 + 0.895828i
\(82\) 3.34000 3.34000i 0.368841 0.368841i
\(83\) 12.2139 12.2139i 1.34065 1.34065i 0.445228 0.895417i \(-0.353123\pi\)
0.895417 0.445228i \(-0.146877\pi\)
\(84\) 0.922931 + 1.65843i 0.100700 + 0.180950i
\(85\) 0 0
\(86\) 5.21490i 0.562337i
\(87\) −4.94920 1.41016i −0.530610 0.151185i
\(88\) −1.74620 1.74620i −0.186145 0.186145i
\(89\) −1.35643 −0.143782 −0.0718908 0.997413i \(-0.522903\pi\)
−0.0718908 + 0.997413i \(0.522903\pi\)
\(90\) 0 0
\(91\) −6.37653 −0.668442
\(92\) 4.12069 + 4.12069i 0.429611 + 0.429611i
\(93\) 9.65754 + 2.75170i 1.00144 + 0.285338i
\(94\) 0.0891871i 0.00919895i
\(95\) 0 0
\(96\) −4.71611 8.47447i −0.481336 0.864922i
\(97\) −10.9812 + 10.9812i −1.11497 + 1.11497i −0.122503 + 0.992468i \(0.539092\pi\)
−0.992468 + 0.122503i \(0.960908\pi\)
\(98\) 1.24414 1.24414i 0.125677 0.125677i
\(99\) 2.45435 3.95731i 0.246671 0.397724i
\(100\) 0 0
\(101\) 12.7033i 1.26402i −0.774958 0.632012i \(-0.782229\pi\)
0.774958 0.632012i \(-0.217771\pi\)
\(102\) 2.51988 8.84392i 0.249505 0.875679i
\(103\) 1.46798 + 1.46798i 0.144644 + 0.144644i 0.775721 0.631076i \(-0.217387\pi\)
−0.631076 + 0.775721i \(0.717387\pi\)
\(104\) 10.1448 0.994779
\(105\) 0 0
\(106\) −10.7203 −1.04125
\(107\) −13.5523 13.5523i −1.31015 1.31015i −0.921302 0.388849i \(-0.872873\pi\)
−0.388849 0.921302i \(-0.627127\pi\)
\(108\) 4.21209 3.83120i 0.405309 0.368658i
\(109\) 4.84158i 0.463739i −0.972747 0.231869i \(-0.925516\pi\)
0.972747 0.231869i \(-0.0744842\pi\)
\(110\) 0 0
\(111\) −2.63530 + 1.46656i −0.250132 + 0.139200i
\(112\) −3.52905 + 3.52905i −0.333464 + 0.333464i
\(113\) −10.6222 + 10.6222i −0.999254 + 0.999254i −1.00000 0.000746132i \(-0.999762\pi\)
0.000746132 1.00000i \(0.499762\pi\)
\(114\) 11.2107 6.23886i 1.04998 0.584323i
\(115\) 0 0
\(116\) 3.25572i 0.302286i
\(117\) 4.36583 + 18.6247i 0.403621 + 1.72186i
\(118\) −6.14308 6.14308i −0.565516 0.565516i
\(119\) −3.01751 −0.276615
\(120\) 0 0
\(121\) 8.59066 0.780969
\(122\) 4.12665 + 4.12665i 0.373610 + 0.373610i
\(123\) −1.27415 + 4.47185i −0.114887 + 0.403213i
\(124\) 6.35300i 0.570517i
\(125\) 0 0
\(126\) −4.48575 2.78209i −0.399623 0.247849i
\(127\) −10.1595 + 10.1595i −0.901511 + 0.901511i −0.995567 0.0940560i \(-0.970017\pi\)
0.0940560 + 0.995567i \(0.470017\pi\)
\(128\) 8.08003 8.08003i 0.714180 0.714180i
\(129\) −2.49636 4.48575i −0.219792 0.394948i
\(130\) 0 0
\(131\) 0.509374i 0.0445042i 0.999752 + 0.0222521i \(0.00708365\pi\)
−0.999752 + 0.0222521i \(0.992916\pi\)
\(132\) −2.83324 0.807270i −0.246602 0.0702638i
\(133\) −2.97687 2.97687i −0.258127 0.258127i
\(134\) −4.25516 −0.367590
\(135\) 0 0
\(136\) 4.80074 0.411660
\(137\) −2.61947 2.61947i −0.223797 0.223797i 0.586298 0.810095i \(-0.300585\pi\)
−0.810095 + 0.586298i \(0.800585\pi\)
\(138\) −15.5868 4.44112i −1.32684 0.378053i
\(139\) 6.35379i 0.538921i 0.963011 + 0.269461i \(0.0868454\pi\)
−0.963011 + 0.269461i \(0.913155\pi\)
\(140\) 0 0
\(141\) −0.0426936 0.0767170i −0.00359545 0.00646074i
\(142\) 7.13612 7.13612i 0.598850 0.598850i
\(143\) 6.99872 6.99872i 0.585262 0.585262i
\(144\) 12.7240 + 7.89149i 1.06033 + 0.657624i
\(145\) 0 0
\(146\) 18.0843i 1.49666i
\(147\) −0.474620 + 1.66575i −0.0391460 + 0.137389i
\(148\) 1.34916 + 1.34916i 0.110900 + 0.110900i
\(149\) 4.27965 0.350602 0.175301 0.984515i \(-0.443910\pi\)
0.175301 + 0.984515i \(0.443910\pi\)
\(150\) 0 0
\(151\) −5.21232 −0.424172 −0.212086 0.977251i \(-0.568026\pi\)
−0.212086 + 0.977251i \(0.568026\pi\)
\(152\) 4.73607 + 4.73607i 0.384146 + 0.384146i
\(153\) 2.06601 + 8.81363i 0.167027 + 0.712539i
\(154\) 2.73108i 0.220077i
\(155\) 0 0
\(156\) 10.5750 5.88509i 0.846681 0.471185i
\(157\) 4.35999 4.35999i 0.347965 0.347965i −0.511386 0.859351i \(-0.670868\pi\)
0.859351 + 0.511386i \(0.170868\pi\)
\(158\) −4.47119 + 4.47119i −0.355708 + 0.355708i
\(159\) 9.22143 5.13179i 0.731307 0.406978i
\(160\) 0 0
\(161\) 5.31816i 0.419129i
\(162\) −5.05474 + 15.0069i −0.397138 + 1.17906i
\(163\) −5.34339 5.34339i −0.418527 0.418527i 0.466169 0.884696i \(-0.345634\pi\)
−0.884696 + 0.466169i \(0.845634\pi\)
\(164\) 2.94171 0.229709
\(165\) 0 0
\(166\) 30.3916 2.35884
\(167\) 13.8232 + 13.8232i 1.06967 + 1.06967i 0.997384 + 0.0722908i \(0.0230310\pi\)
0.0722908 + 0.997384i \(0.476969\pi\)
\(168\) 0.755101 2.65015i 0.0582573 0.204463i
\(169\) 27.6601i 2.12770i
\(170\) 0 0
\(171\) −6.65673 + 10.7331i −0.509053 + 0.820780i
\(172\) −2.29651 + 2.29651i −0.175108 + 0.175108i
\(173\) −2.06635 + 2.06635i −0.157102 + 0.157102i −0.781281 0.624179i \(-0.785433\pi\)
0.624179 + 0.781281i \(0.285433\pi\)
\(174\) −4.40306 7.91195i −0.333795 0.599803i
\(175\) 0 0
\(176\) 7.74679i 0.583936i
\(177\) 8.22483 + 2.34348i 0.618216 + 0.176147i
\(178\) −1.68759 1.68759i −0.126491 0.126491i
\(179\) 11.9186 0.890841 0.445420 0.895322i \(-0.353054\pi\)
0.445420 + 0.895322i \(0.353054\pi\)
\(180\) 0 0
\(181\) −17.5945 −1.30779 −0.653893 0.756587i \(-0.726865\pi\)
−0.653893 + 0.756587i \(0.726865\pi\)
\(182\) −7.93331 7.93331i −0.588056 0.588056i
\(183\) −5.52508 1.57425i −0.408426 0.116372i
\(184\) 8.46097i 0.623751i
\(185\) 0 0
\(186\) 8.59184 + 15.4389i 0.629985 + 1.13203i
\(187\) 3.31195 3.31195i 0.242194 0.242194i
\(188\) −0.0392758 + 0.0392758i −0.00286449 + 0.00286449i
\(189\) 5.19034 + 0.245787i 0.377541 + 0.0178783i
\(190\) 0 0
\(191\) 5.54023i 0.400877i 0.979706 + 0.200438i \(0.0642366\pi\)
−0.979706 + 0.200438i \(0.935763\pi\)
\(192\) −0.0615505 + 0.216021i −0.00444202 + 0.0155900i
\(193\) 13.9027 + 13.9027i 1.00074 + 1.00074i 1.00000 0.000740397i \(0.000235676\pi\)
0.000740397 1.00000i \(0.499764\pi\)
\(194\) −27.3243 −1.96177
\(195\) 0 0
\(196\) 1.09578 0.0782700
\(197\) −12.7155 12.7155i −0.905939 0.905939i 0.0900024 0.995942i \(-0.471313\pi\)
−0.995942 + 0.0900024i \(0.971313\pi\)
\(198\) 7.97701 1.86989i 0.566901 0.132888i
\(199\) 6.11487i 0.433472i −0.976230 0.216736i \(-0.930459\pi\)
0.976230 0.216736i \(-0.0695411\pi\)
\(200\) 0 0
\(201\) 3.66021 2.03693i 0.258171 0.143674i
\(202\) 15.8047 15.8047i 1.11201 1.11201i
\(203\) −2.10092 + 2.10092i −0.147455 + 0.147455i
\(204\) 5.00434 2.78495i 0.350374 0.194986i
\(205\) 0 0
\(206\) 3.65275i 0.254499i
\(207\) 15.5334 3.64119i 1.07965 0.253080i
\(208\) 22.5031 + 22.5031i 1.56031 + 1.56031i
\(209\) 6.53467 0.452013
\(210\) 0 0
\(211\) 12.4900 0.859849 0.429924 0.902865i \(-0.358540\pi\)
0.429924 + 0.902865i \(0.358540\pi\)
\(212\) −4.72098 4.72098i −0.324238 0.324238i
\(213\) −2.72231 + 9.55439i −0.186530 + 0.654656i
\(214\) 33.7220i 2.30519i
\(215\) 0 0
\(216\) −8.25761 0.391036i −0.561859 0.0266067i
\(217\) 4.09959 4.09959i 0.278298 0.278298i
\(218\) 6.02361 6.02361i 0.407970 0.407970i
\(219\) 8.65688 + 15.5557i 0.584978 + 1.05116i
\(220\) 0 0
\(221\) 19.2412i 1.29431i
\(222\) −5.10330 1.45407i −0.342511 0.0975910i
\(223\) −8.80424 8.80424i −0.589576 0.589576i 0.347941 0.937516i \(-0.386881\pi\)
−0.937516 + 0.347941i \(0.886881\pi\)
\(224\) −5.59935 −0.374123
\(225\) 0 0
\(226\) −26.4311 −1.75817
\(227\) −15.7424 15.7424i −1.04486 1.04486i −0.998945 0.0459126i \(-0.985380\pi\)
−0.0459126 0.998945i \(-0.514620\pi\)
\(228\) 7.68438 + 2.18949i 0.508910 + 0.145003i
\(229\) 8.27446i 0.546791i −0.961902 0.273396i \(-0.911853\pi\)
0.961902 0.273396i \(-0.0881468\pi\)
\(230\) 0 0
\(231\) −1.30736 2.34922i −0.0860179 0.154567i
\(232\) 3.34247 3.34247i 0.219444 0.219444i
\(233\) −12.6425 + 12.6425i −0.828239 + 0.828239i −0.987273 0.159034i \(-0.949162\pi\)
0.159034 + 0.987273i \(0.449162\pi\)
\(234\) −17.7401 + 28.6035i −1.15971 + 1.86987i
\(235\) 0 0
\(236\) 5.41052i 0.352195i
\(237\) 1.70568 5.98637i 0.110796 0.388856i
\(238\) −3.75421 3.75421i −0.243350 0.243350i
\(239\) −25.8260 −1.67054 −0.835271 0.549838i \(-0.814689\pi\)
−0.835271 + 0.549838i \(0.814689\pi\)
\(240\) 0 0
\(241\) −10.5197 −0.677631 −0.338815 0.940853i \(-0.610026\pi\)
−0.338815 + 0.940853i \(0.610026\pi\)
\(242\) 10.6880 + 10.6880i 0.687051 + 0.687051i
\(243\) −2.83578 15.3284i −0.181915 0.983314i
\(244\) 3.63456i 0.232679i
\(245\) 0 0
\(246\) −7.14885 + 3.97839i −0.455794 + 0.253653i
\(247\) −18.9821 + 18.9821i −1.20780 + 1.20780i
\(248\) −6.52229 + 6.52229i −0.414166 + 0.414166i
\(249\) −26.1422 + 14.5483i −1.65670 + 0.921964i
\(250\) 0 0
\(251\) 6.94563i 0.438405i 0.975679 + 0.219202i \(0.0703455\pi\)
−0.975679 + 0.219202i \(0.929655\pi\)
\(252\) −0.750250 3.20058i −0.0472613 0.201618i
\(253\) −5.83708 5.83708i −0.366974 0.366974i
\(254\) −25.2798 −1.58619
\(255\) 0 0
\(256\) 19.8460 1.24038
\(257\) −8.17057 8.17057i −0.509666 0.509666i 0.404758 0.914424i \(-0.367356\pi\)
−0.914424 + 0.404758i \(0.867356\pi\)
\(258\) 2.47509 8.68674i 0.154093 0.540813i
\(259\) 1.74123i 0.108195i
\(260\) 0 0
\(261\) 7.57485 + 4.69797i 0.468872 + 0.290797i
\(262\) −0.633733 + 0.633733i −0.0391522 + 0.0391522i
\(263\) −0.118860 + 0.118860i −0.00732922 + 0.00732922i −0.710762 0.703433i \(-0.751650\pi\)
0.703433 + 0.710762i \(0.251650\pi\)
\(264\) 2.07996 + 3.73752i 0.128012 + 0.230028i
\(265\) 0 0
\(266\) 7.40729i 0.454170i
\(267\) 2.25948 + 0.643790i 0.138278 + 0.0393993i
\(268\) −1.87387 1.87387i −0.114465 0.114465i
\(269\) 6.60330 0.402610 0.201305 0.979529i \(-0.435482\pi\)
0.201305 + 0.979529i \(0.435482\pi\)
\(270\) 0 0
\(271\) −23.8292 −1.44752 −0.723759 0.690052i \(-0.757587\pi\)
−0.723759 + 0.690052i \(0.757587\pi\)
\(272\) 10.6489 + 10.6489i 0.645687 + 0.645687i
\(273\) 10.6217 + 3.02643i 0.642856 + 0.183168i
\(274\) 6.51800i 0.393767i
\(275\) 0 0
\(276\) −4.90829 8.81981i −0.295444 0.530890i
\(277\) 14.3921 14.3921i 0.864736 0.864736i −0.127147 0.991884i \(-0.540582\pi\)
0.991884 + 0.127147i \(0.0405821\pi\)
\(278\) −7.90501 + 7.90501i −0.474111 + 0.474111i
\(279\) −14.7811 9.16732i −0.884920 0.548833i
\(280\) 0 0
\(281\) 1.50698i 0.0898991i −0.998989 0.0449495i \(-0.985687\pi\)
0.998989 0.0449495i \(-0.0143127\pi\)
\(282\) 0.0423300 0.148564i 0.00252071 0.00884685i
\(283\) −8.49114 8.49114i −0.504746 0.504746i 0.408163 0.912909i \(-0.366170\pi\)
−0.912909 + 0.408163i \(0.866170\pi\)
\(284\) 6.28515 0.372955
\(285\) 0 0
\(286\) 17.4148 1.02976
\(287\) 1.89828 + 1.89828i 0.112052 + 0.112052i
\(288\) 3.83372 + 16.3547i 0.225904 + 0.963712i
\(289\) 7.89463i 0.464390i
\(290\) 0 0
\(291\) 23.5039 13.0801i 1.37782 0.766768i
\(292\) 7.96387 7.96387i 0.466050 0.466050i
\(293\) 2.35851 2.35851i 0.137786 0.137786i −0.634850 0.772635i \(-0.718938\pi\)
0.772635 + 0.634850i \(0.218938\pi\)
\(294\) −2.66293 + 1.48194i −0.155305 + 0.0864285i
\(295\) 0 0
\(296\) 2.77022i 0.161016i
\(297\) −5.96656 + 5.42702i −0.346215 + 0.314907i
\(298\) 5.32449 + 5.32449i 0.308439 + 0.308439i
\(299\) 33.9114 1.96115
\(300\) 0 0
\(301\) −2.96388 −0.170835
\(302\) −6.48486 6.48486i −0.373162 0.373162i
\(303\) −6.02923 + 21.1606i −0.346370 + 1.21564i
\(304\) 21.0110i 1.20506i
\(305\) 0 0
\(306\) −8.39500 + 13.5358i −0.479910 + 0.773791i
\(307\) 0.793602 0.793602i 0.0452933 0.0452933i −0.684097 0.729391i \(-0.739804\pi\)
0.729391 + 0.684097i \(0.239804\pi\)
\(308\) −1.20270 + 1.20270i −0.0685303 + 0.0685303i
\(309\) −1.74856 3.14203i −0.0994722 0.178744i
\(310\) 0 0
\(311\) 9.91521i 0.562240i −0.959673 0.281120i \(-0.909294\pi\)
0.959673 0.281120i \(-0.0907059\pi\)
\(312\) −16.8987 4.81492i −0.956702 0.272591i
\(313\) 9.95137 + 9.95137i 0.562484 + 0.562484i 0.930012 0.367528i \(-0.119796\pi\)
−0.367528 + 0.930012i \(0.619796\pi\)
\(314\) 10.8489 0.612238
\(315\) 0 0
\(316\) −3.93800 −0.221530
\(317\) 14.9788 + 14.9788i 0.841296 + 0.841296i 0.989027 0.147732i \(-0.0471972\pi\)
−0.147732 + 0.989027i \(0.547197\pi\)
\(318\) 17.8574 + 5.08809i 1.00140 + 0.285326i
\(319\) 4.61183i 0.258213i
\(320\) 0 0
\(321\) 16.1426 + 29.0070i 0.900992 + 1.61901i
\(322\) −6.61654 + 6.61654i −0.368726 + 0.368726i
\(323\) −8.98273 + 8.98273i −0.499812 + 0.499812i
\(324\) −8.83467 + 4.38270i −0.490815 + 0.243483i
\(325\) 0 0
\(326\) 13.2959i 0.736391i
\(327\) −2.29791 + 8.06487i −0.127075 + 0.445989i
\(328\) −3.02009 3.02009i −0.166757 0.166757i
\(329\) −0.0506894 −0.00279460
\(330\) 0 0
\(331\) −3.10247 −0.170527 −0.0852635 0.996358i \(-0.527173\pi\)
−0.0852635 + 0.996358i \(0.527173\pi\)
\(332\) 13.3837 + 13.3837i 0.734526 + 0.734526i
\(333\) 5.08582 1.19217i 0.278701 0.0653305i
\(334\) 34.3962i 1.88207i
\(335\) 0 0
\(336\) 7.55348 4.20357i 0.412076 0.229323i
\(337\) 23.2030 23.2030i 1.26395 1.26395i 0.314784 0.949163i \(-0.398068\pi\)
0.949163 0.314784i \(-0.101932\pi\)
\(338\) −34.4131 + 34.4131i −1.87183 + 1.87183i
\(339\) 22.7355 12.6525i 1.23482 0.687188i
\(340\) 0 0
\(341\) 8.99922i 0.487335i
\(342\) −21.6354 + 5.07157i −1.16991 + 0.274239i
\(343\) 0.707107 + 0.707107i 0.0381802 + 0.0381802i
\(344\) 4.71541 0.254238
\(345\) 0 0
\(346\) −5.14167 −0.276418
\(347\) 14.1837 + 14.1837i 0.761423 + 0.761423i 0.976580 0.215157i \(-0.0690262\pi\)
−0.215157 + 0.976580i \(0.569026\pi\)
\(348\) 1.54523 5.42323i 0.0828330 0.290716i
\(349\) 9.27152i 0.496293i 0.968723 + 0.248146i \(0.0798214\pi\)
−0.968723 + 0.248146i \(0.920179\pi\)
\(350\) 0 0
\(351\) 1.56726 33.0963i 0.0836544 1.76655i
\(352\) 6.14571 6.14571i 0.327568 0.327568i
\(353\) 20.2421 20.2421i 1.07738 1.07738i 0.0806368 0.996744i \(-0.474305\pi\)
0.996744 0.0806368i \(-0.0256954\pi\)
\(354\) 7.31723 + 13.1485i 0.388906 + 0.698834i
\(355\) 0 0
\(356\) 1.48635i 0.0787765i
\(357\) 5.02643 + 1.43217i 0.266027 + 0.0757985i
\(358\) 14.8285 + 14.8285i 0.783710 + 0.783710i
\(359\) −18.8289 −0.993751 −0.496876 0.867822i \(-0.665519\pi\)
−0.496876 + 0.867822i \(0.665519\pi\)
\(360\) 0 0
\(361\) 1.27653 0.0671857
\(362\) −21.8900 21.8900i −1.15051 1.15051i
\(363\) −14.3099 4.07730i −0.751076 0.214003i
\(364\) 6.98727i 0.366233i
\(365\) 0 0
\(366\) −4.91540 8.83258i −0.256932 0.461686i
\(367\) −0.942012 + 0.942012i −0.0491726 + 0.0491726i −0.731266 0.682093i \(-0.761070\pi\)
0.682093 + 0.731266i \(0.261070\pi\)
\(368\) 18.7680 18.7680i 0.978351 0.978351i
\(369\) 4.24486 6.84426i 0.220978 0.356298i
\(370\) 0 0
\(371\) 6.09289i 0.316327i
\(372\) −3.01526 + 10.5825i −0.156334 + 0.548679i
\(373\) −7.39940 7.39940i −0.383127 0.383127i 0.489101 0.872227i \(-0.337325\pi\)
−0.872227 + 0.489101i \(0.837325\pi\)
\(374\) 8.24107 0.426135
\(375\) 0 0
\(376\) 0.0806448 0.00415894
\(377\) 13.3966 + 13.3966i 0.689958 + 0.689958i
\(378\) 6.15172 + 6.76331i 0.316411 + 0.347867i
\(379\) 21.9486i 1.12743i −0.825971 0.563713i \(-0.809373\pi\)
0.825971 0.563713i \(-0.190627\pi\)
\(380\) 0 0
\(381\) 21.7452 12.1013i 1.11404 0.619970i
\(382\) −6.89283 + 6.89283i −0.352668 + 0.352668i
\(383\) 19.3310 19.3310i 0.987768 0.987768i −0.0121580 0.999926i \(-0.503870\pi\)
0.999926 + 0.0121580i \(0.00387012\pi\)
\(384\) −17.2943 + 9.62440i −0.882545 + 0.491143i
\(385\) 0 0
\(386\) 34.5939i 1.76079i
\(387\) 2.02929 + 8.65698i 0.103154 + 0.440059i
\(388\) −12.0330 12.0330i −0.610882 0.610882i
\(389\) 30.7961 1.56142 0.780712 0.624891i \(-0.214856\pi\)
0.780712 + 0.624891i \(0.214856\pi\)
\(390\) 0 0
\(391\) 16.0476 0.811562
\(392\) −1.12498 1.12498i −0.0568200 0.0568200i
\(393\) 0.241759 0.848491i 0.0121951 0.0428007i
\(394\) 31.6397i 1.59398i
\(395\) 0 0
\(396\) 4.33634 + 2.68943i 0.217909 + 0.135149i
\(397\) 20.8254 20.8254i 1.04520 1.04520i 0.0462702 0.998929i \(-0.485266\pi\)
0.998929 0.0462702i \(-0.0147335\pi\)
\(398\) 7.60777 7.60777i 0.381343 0.381343i
\(399\) 3.54585 + 6.37161i 0.177514 + 0.318979i
\(400\) 0 0
\(401\) 20.9084i 1.04412i 0.852910 + 0.522058i \(0.174835\pi\)
−0.852910 + 0.522058i \(0.825165\pi\)
\(402\) 7.08805 + 2.01958i 0.353520 + 0.100728i
\(403\) −26.1412 26.1412i −1.30218 1.30218i
\(404\) 13.9200 0.692547
\(405\) 0 0
\(406\) −5.22768 −0.259445
\(407\) −1.91113 1.91113i −0.0947311 0.0947311i
\(408\) −7.99685 2.27853i −0.395903 0.112804i
\(409\) 11.5773i 0.572460i −0.958161 0.286230i \(-0.907598\pi\)
0.958161 0.286230i \(-0.0924022\pi\)
\(410\) 0 0
\(411\) 3.12014 + 5.60665i 0.153905 + 0.276556i
\(412\) −1.60858 + 1.60858i −0.0792493 + 0.0792493i
\(413\) 3.49141 3.49141i 0.171801 0.171801i
\(414\) 23.8559 + 14.7956i 1.17246 + 0.727165i
\(415\) 0 0
\(416\) 35.7044i 1.75055i
\(417\) 3.01563 10.5838i 0.147676 0.518293i
\(418\) 8.13006 + 8.13006i 0.397654 + 0.397654i
\(419\) −0.525515 −0.0256731 −0.0128365 0.999918i \(-0.504086\pi\)
−0.0128365 + 0.999918i \(0.504086\pi\)
\(420\) 0 0
\(421\) −15.5297 −0.756871 −0.378435 0.925628i \(-0.623538\pi\)
−0.378435 + 0.925628i \(0.623538\pi\)
\(422\) 15.5394 + 15.5394i 0.756445 + 0.756445i
\(423\) 0.0347056 + 0.148055i 0.00168744 + 0.00719868i
\(424\) 9.69354i 0.470760i
\(425\) 0 0
\(426\) −15.2740 + 8.50008i −0.740026 + 0.411830i
\(427\) −2.34538 + 2.34538i −0.113501 + 0.113501i
\(428\) 14.8503 14.8503i 0.717818 0.717818i
\(429\) −14.9799 + 8.33641i −0.723235 + 0.402486i
\(430\) 0 0
\(431\) 23.0144i 1.10856i −0.832329 0.554282i \(-0.812993\pi\)
0.832329 0.554282i \(-0.187007\pi\)
\(432\) −17.4495 19.1843i −0.839542 0.923007i
\(433\) 15.4001 + 15.4001i 0.740081 + 0.740081i 0.972593 0.232513i \(-0.0746947\pi\)
−0.232513 + 0.972593i \(0.574695\pi\)
\(434\) 10.2010 0.489661
\(435\) 0 0
\(436\) 5.30530 0.254078
\(437\) 15.8314 + 15.8314i 0.757321 + 0.757321i
\(438\) −8.58315 + 30.1239i −0.410119 + 1.43938i
\(439\) 6.04288i 0.288411i 0.989548 + 0.144205i \(0.0460626\pi\)
−0.989548 + 0.144205i \(0.953937\pi\)
\(440\) 0 0
\(441\) 1.58120 2.54947i 0.0752952 0.121403i
\(442\) −23.9388 + 23.9388i −1.13865 + 1.13865i
\(443\) 8.64725 8.64725i 0.410843 0.410843i −0.471189 0.882032i \(-0.656175\pi\)
0.882032 + 0.471189i \(0.156175\pi\)
\(444\) −1.60703 2.88771i −0.0762664 0.137045i
\(445\) 0 0
\(446\) 21.9075i 1.03735i
\(447\) −7.12884 2.03121i −0.337183 0.0960727i
\(448\) 0.0917003 + 0.0917003i 0.00433243 + 0.00433243i
\(449\) −20.7599 −0.979723 −0.489861 0.871800i \(-0.662953\pi\)
−0.489861 + 0.871800i \(0.662953\pi\)
\(450\) 0 0
\(451\) −4.16702 −0.196217
\(452\) −11.6396 11.6396i −0.547481 0.547481i
\(453\) 8.68243 + 2.47387i 0.407936 + 0.116232i
\(454\) 39.1715i 1.83841i
\(455\) 0 0
\(456\) −5.64130 10.1370i −0.264178 0.474707i
\(457\) −17.3075 + 17.3075i −0.809612 + 0.809612i −0.984575 0.174963i \(-0.944020\pi\)
0.174963 + 0.984575i \(0.444020\pi\)
\(458\) 10.2946 10.2946i 0.481035 0.481035i
\(459\) 0.741664 15.6619i 0.0346179 0.731035i
\(460\) 0 0
\(461\) 4.36421i 0.203262i −0.994822 0.101631i \(-0.967594\pi\)
0.994822 0.101631i \(-0.0324061\pi\)
\(462\) 1.29622 4.54931i 0.0603058 0.211653i
\(463\) −2.04147 2.04147i −0.0948752 0.0948752i 0.658076 0.752951i \(-0.271370\pi\)
−0.752951 + 0.658076i \(0.771370\pi\)
\(464\) 14.8285 0.688394
\(465\) 0 0
\(466\) −31.4582 −1.45727
\(467\) 13.9629 + 13.9629i 0.646128 + 0.646128i 0.952055 0.305927i \(-0.0989663\pi\)
−0.305927 + 0.952055i \(0.598966\pi\)
\(468\) −20.4086 + 4.78399i −0.943388 + 0.221140i
\(469\) 2.41842i 0.111672i
\(470\) 0 0
\(471\) −9.33200 + 5.19333i −0.429996 + 0.239296i
\(472\) −5.55469 + 5.55469i −0.255675 + 0.255675i
\(473\) 3.25308 3.25308i 0.149577 0.149577i
\(474\) 9.57001 5.32578i 0.439565 0.244621i
\(475\) 0 0
\(476\) 3.30653i 0.151555i
\(477\) −17.7963 + 4.17163i −0.814836 + 0.191006i
\(478\) −32.1312 32.1312i −1.46965 1.46965i
\(479\) 16.0067 0.731367 0.365683 0.930739i \(-0.380835\pi\)
0.365683 + 0.930739i \(0.380835\pi\)
\(480\) 0 0
\(481\) 11.1030 0.506252
\(482\) −13.0880 13.0880i −0.596140 0.596140i
\(483\) 2.52410 8.85874i 0.114851 0.403087i
\(484\) 9.41347i 0.427885i
\(485\) 0 0
\(486\) 15.5425 22.5988i 0.705024 1.02510i
\(487\) −20.6096 + 20.6096i −0.933908 + 0.933908i −0.997947 0.0640391i \(-0.979602\pi\)
0.0640391 + 0.997947i \(0.479602\pi\)
\(488\) 3.73140 3.73140i 0.168913 0.168913i
\(489\) 6.36470 + 11.4369i 0.287822 + 0.517192i
\(490\) 0 0
\(491\) 29.8846i 1.34867i 0.738423 + 0.674337i \(0.235571\pi\)
−0.738423 + 0.674337i \(0.764429\pi\)
\(492\) −4.90016 1.39619i −0.220916 0.0629453i
\(493\) 6.33954 + 6.33954i 0.285519 + 0.285519i
\(494\) −47.2328 −2.12510
\(495\) 0 0
\(496\) −28.9353 −1.29923
\(497\) 4.05581 + 4.05581i 0.181928 + 0.181928i
\(498\) −50.6249 14.4244i −2.26855 0.646374i
\(499\) 0.940603i 0.0421072i 0.999778 + 0.0210536i \(0.00670206\pi\)
−0.999778 + 0.0210536i \(0.993298\pi\)
\(500\) 0 0
\(501\) −16.4653 29.5869i −0.735617 1.32185i
\(502\) −8.64136 + 8.64136i −0.385683 + 0.385683i
\(503\) −23.0051 + 23.0051i −1.02575 + 1.02575i −0.0260875 + 0.999660i \(0.508305\pi\)
−0.999660 + 0.0260875i \(0.991695\pi\)
\(504\) −2.51562 + 4.05611i −0.112055 + 0.180673i
\(505\) 0 0
\(506\) 14.5243i 0.645685i
\(507\) 13.1280 46.0749i 0.583036 2.04626i
\(508\) −11.1326 11.1326i −0.493929 0.493929i
\(509\) −25.8128 −1.14413 −0.572066 0.820208i \(-0.693858\pi\)
−0.572066 + 0.820208i \(0.693858\pi\)
\(510\) 0 0
\(511\) 10.2782 0.454679
\(512\) 8.53124 + 8.53124i 0.377031 + 0.377031i
\(513\) 16.1826 14.7193i 0.714480 0.649871i
\(514\) 20.3307i 0.896749i
\(515\) 0 0
\(516\) 4.91540 2.73546i 0.216388 0.120422i
\(517\) 0.0556354 0.0556354i 0.00244684 0.00244684i
\(518\) −2.16633 + 2.16633i −0.0951833 + 0.0951833i
\(519\) 4.42276 2.46130i 0.194138 0.108039i
\(520\) 0 0
\(521\) 44.1826i 1.93568i −0.251572 0.967838i \(-0.580948\pi\)
0.251572 0.967838i \(-0.419052\pi\)
\(522\) 3.57925 + 15.2691i 0.156659 + 0.668312i
\(523\) −13.0685 13.0685i −0.571447 0.571447i 0.361086 0.932533i \(-0.382406\pi\)
−0.932533 + 0.361086i \(0.882406\pi\)
\(524\) −0.558162 −0.0243834
\(525\) 0 0
\(526\) −0.295757 −0.0128956
\(527\) −12.3706 12.3706i −0.538870 0.538870i
\(528\) −3.67678 + 12.9042i −0.160011 + 0.561585i
\(529\) 5.28280i 0.229687i
\(530\) 0 0
\(531\) −12.5883 7.80733i −0.546285 0.338809i
\(532\) 3.26199 3.26199i 0.141425 0.141425i
\(533\) 12.1045 12.1045i 0.524303 0.524303i
\(534\) 2.01015 + 3.61208i 0.0869878 + 0.156310i
\(535\) 0 0
\(536\) 3.84760i 0.166191i
\(537\) −19.8535 5.65682i −0.856743 0.244110i
\(538\) 8.21544 + 8.21544i 0.354193 + 0.354193i
\(539\) −1.55221 −0.0668583
\(540\) 0 0
\(541\) 21.5590 0.926893 0.463446 0.886125i \(-0.346613\pi\)
0.463446 + 0.886125i \(0.346613\pi\)
\(542\) −29.6469 29.6469i −1.27344 1.27344i
\(543\) 29.3080 + 8.35068i 1.25773 + 0.358362i
\(544\) 16.8961i 0.724415i
\(545\) 0 0
\(546\) 9.44963 + 16.9802i 0.404407 + 0.726687i
\(547\) 29.6665 29.6665i 1.26845 1.26845i 0.321555 0.946891i \(-0.395795\pi\)
0.946891 0.321555i \(-0.104205\pi\)
\(548\) 2.87037 2.87037i 0.122616 0.122616i
\(549\) 8.45626 + 5.24463i 0.360904 + 0.223835i
\(550\) 0 0
\(551\) 12.5083i 0.532872i
\(552\) −4.01574 + 14.0939i −0.170921 + 0.599876i
\(553\) −2.54119 2.54119i −0.108063 0.108063i
\(554\) 35.8116 1.52149
\(555\) 0 0
\(556\) −6.96235 −0.295269
\(557\) −19.2396 19.2396i −0.815208 0.815208i 0.170201 0.985409i \(-0.445558\pi\)
−0.985409 + 0.170201i \(0.945558\pi\)
\(558\) −6.98431 29.7952i −0.295669 1.26133i
\(559\) 18.8993i 0.799354i
\(560\) 0 0
\(561\) −7.08880 + 3.94497i −0.299290 + 0.166557i
\(562\) 1.87490 1.87490i 0.0790880 0.0790880i
\(563\) 2.03574 2.03574i 0.0857962 0.0857962i −0.662906 0.748702i \(-0.730677\pi\)
0.748702 + 0.662906i \(0.230677\pi\)
\(564\) 0.0840650 0.0467828i 0.00353977 0.00196991i
\(565\) 0 0
\(566\) 21.1284i 0.888092i
\(567\) −8.52917 2.87286i −0.358191 0.120649i
\(568\) −6.45262 6.45262i −0.270746 0.270746i
\(569\) −36.6125 −1.53487 −0.767437 0.641124i \(-0.778468\pi\)
−0.767437 + 0.641124i \(0.778468\pi\)
\(570\) 0 0
\(571\) −9.88863 −0.413826 −0.206913 0.978359i \(-0.566342\pi\)
−0.206913 + 0.978359i \(0.566342\pi\)
\(572\) 7.66906 + 7.66906i 0.320659 + 0.320659i
\(573\) 2.62950 9.22865i 0.109849 0.385533i
\(574\) 4.72347i 0.197154i
\(575\) 0 0
\(576\) 0.205056 0.330625i 0.00854400 0.0137760i
\(577\) −3.44953 + 3.44953i −0.143606 + 0.143606i −0.775255 0.631649i \(-0.782378\pi\)
0.631649 + 0.775255i \(0.282378\pi\)
\(578\) 9.82204 9.82204i 0.408543 0.408543i
\(579\) −16.5600 29.7570i −0.688211 1.23666i
\(580\) 0 0
\(581\) 17.2730i 0.716605i
\(582\) 45.5156 + 12.9687i 1.88668 + 0.537569i
\(583\) 6.68741 + 6.68741i 0.276964 + 0.276964i
\(584\) −16.3521 −0.676657
\(585\) 0 0
\(586\) 5.86864 0.242431
\(587\) 4.70846 + 4.70846i 0.194339 + 0.194339i 0.797568 0.603229i \(-0.206120\pi\)
−0.603229 + 0.797568i \(0.706120\pi\)
\(588\) −1.82530 0.520079i −0.0752741 0.0214477i
\(589\) 24.4079i 1.00571i
\(590\) 0 0
\(591\) 15.1458 + 27.2158i 0.623016 + 1.11951i
\(592\) 6.14487 6.14487i 0.252553 0.252553i
\(593\) −15.2900 + 15.2900i −0.627884 + 0.627884i −0.947535 0.319651i \(-0.896434\pi\)
0.319651 + 0.947535i \(0.396434\pi\)
\(594\) −14.1752 0.671263i −0.581617 0.0275422i
\(595\) 0 0
\(596\) 4.68955i 0.192092i
\(597\) −2.90224 + 10.1859i −0.118781 + 0.416880i
\(598\) 42.1906 + 42.1906i 1.72530 + 1.72530i
\(599\) 9.38844 0.383601 0.191801 0.981434i \(-0.438567\pi\)
0.191801 + 0.981434i \(0.438567\pi\)
\(600\) 0 0
\(601\) −4.87361 −0.198799 −0.0993993 0.995048i \(-0.531692\pi\)
−0.0993993 + 0.995048i \(0.531692\pi\)
\(602\) −3.68749 3.68749i −0.150291 0.150291i
\(603\) −7.06377 + 1.65582i −0.287659 + 0.0674303i
\(604\) 5.71155i 0.232400i
\(605\) 0 0
\(606\) −33.8280 + 18.8255i −1.37417 + 0.764734i
\(607\) 2.56287 2.56287i 0.104024 0.104024i −0.653180 0.757203i \(-0.726565\pi\)
0.757203 + 0.653180i \(0.226565\pi\)
\(608\) −16.6685 + 16.6685i −0.675998 + 0.675998i
\(609\) 4.49675 2.50247i 0.182217 0.101405i
\(610\) 0 0
\(611\) 0.323222i 0.0130762i
\(612\) −9.65780 + 2.26389i −0.390393 + 0.0915123i
\(613\) −33.5166 33.5166i −1.35372 1.35372i −0.881457 0.472264i \(-0.843437\pi\)
−0.472264 0.881457i \(-0.656563\pi\)
\(614\) 1.97471 0.0796927
\(615\) 0 0
\(616\) 2.46950 0.0994989
\(617\) −2.15297 2.15297i −0.0866754 0.0866754i 0.662440 0.749115i \(-0.269521\pi\)
−0.749115 + 0.662440i \(0.769521\pi\)
\(618\) 1.73367 6.08459i 0.0697384 0.244758i
\(619\) 10.1941i 0.409737i −0.978789 0.204869i \(-0.934323\pi\)
0.978789 0.204869i \(-0.0656767\pi\)
\(620\) 0 0
\(621\) −27.6030 1.30713i −1.10767 0.0524534i
\(622\) 12.3359 12.3359i 0.494626 0.494626i
\(623\) 0.959142 0.959142i 0.0384272 0.0384272i
\(624\) −26.8042 48.1650i −1.07303 1.92814i
\(625\) 0 0
\(626\) 24.7618i 0.989682i
\(627\) −10.8852 3.10148i −0.434711 0.123861i
\(628\) 4.77759 + 4.77759i 0.190646 + 0.190646i
\(629\) 5.25417 0.209498
\(630\) 0 0
\(631\) 44.6402 1.77710 0.888550 0.458781i \(-0.151714\pi\)
0.888550 + 0.458781i \(0.151714\pi\)
\(632\) 4.04293 + 4.04293i 0.160819 + 0.160819i
\(633\) −20.8053 5.92801i −0.826937 0.235617i
\(634\) 37.2716i 1.48025i
\(635\) 0 0
\(636\) 5.62332 + 10.1047i 0.222979 + 0.400676i
\(637\) 4.50889 4.50889i 0.178649 0.178649i
\(638\) 5.73777 5.73777i 0.227161 0.227161i
\(639\) 9.06940 14.6232i 0.358780 0.578485i
\(640\) 0 0
\(641\) 15.7329i 0.621414i 0.950506 + 0.310707i \(0.100566\pi\)
−0.950506 + 0.310707i \(0.899434\pi\)
\(642\) −16.0051 + 56.1725i −0.631672 + 2.21695i
\(643\) 11.7811 + 11.7811i 0.464600 + 0.464600i 0.900160 0.435560i \(-0.143449\pi\)
−0.435560 + 0.900160i \(0.643449\pi\)
\(644\) −5.82753 −0.229637
\(645\) 0 0
\(646\) −22.3516 −0.879411
\(647\) −10.8002 10.8002i −0.424600 0.424600i 0.462184 0.886784i \(-0.347066\pi\)
−0.886784 + 0.462184i \(0.847066\pi\)
\(648\) 13.5696 + 4.57060i 0.533063 + 0.179550i
\(649\) 7.66417i 0.300845i
\(650\) 0 0
\(651\) −8.77466 + 4.88316i −0.343906 + 0.191386i
\(652\) 5.85518 5.85518i 0.229307 0.229307i
\(653\) −7.88328 + 7.88328i −0.308497 + 0.308497i −0.844326 0.535830i \(-0.819999\pi\)
0.535830 + 0.844326i \(0.319999\pi\)
\(654\) −12.8928 + 7.17493i −0.504147 + 0.280562i
\(655\) 0 0
\(656\) 13.3983i 0.523115i
\(657\) −7.03717 30.0207i −0.274546 1.17122i
\(658\) −0.0630648 0.0630648i −0.00245852 0.00245852i
\(659\) 6.73141 0.262219 0.131109 0.991368i \(-0.458146\pi\)
0.131109 + 0.991368i \(0.458146\pi\)
\(660\) 0 0
\(661\) 4.43191 0.172381 0.0861906 0.996279i \(-0.472531\pi\)
0.0861906 + 0.996279i \(0.472531\pi\)
\(662\) −3.85991 3.85991i −0.150020 0.150020i
\(663\) 9.13228 32.0512i 0.354668 1.24476i
\(664\) 27.4807i 1.06646i
\(665\) 0 0
\(666\) 7.81072 + 4.84426i 0.302659 + 0.187711i
\(667\) 11.1730 11.1730i 0.432621 0.432621i
\(668\) −15.1472 + 15.1472i −0.586064 + 0.586064i
\(669\) 10.4870 + 18.8444i 0.405452 + 0.728565i
\(670\) 0 0
\(671\) 5.14846i 0.198754i
\(672\) 9.32715 + 2.65756i 0.359802 + 0.102518i
\(673\) 3.35642 + 3.35642i 0.129381 + 0.129381i 0.768832 0.639451i \(-0.220838\pi\)
−0.639451 + 0.768832i \(0.720838\pi\)
\(674\) 57.7356 2.22389
\(675\) 0 0
\(676\) −30.3094 −1.16575
\(677\) 6.31136 + 6.31136i 0.242565 + 0.242565i 0.817911 0.575345i \(-0.195132\pi\)
−0.575345 + 0.817911i \(0.695132\pi\)
\(678\) 44.0277 + 12.5447i 1.69087 + 0.481777i
\(679\) 15.5298i 0.595977i
\(680\) 0 0
\(681\) 18.7513 + 33.6946i 0.718551 + 1.29118i
\(682\) −11.1963 + 11.1963i −0.428729 + 0.428729i
\(683\) −21.4480 + 21.4480i −0.820686 + 0.820686i −0.986206 0.165520i \(-0.947070\pi\)
0.165520 + 0.986206i \(0.447070\pi\)
\(684\) −11.7611 7.29431i −0.449697 0.278905i
\(685\) 0 0
\(686\) 1.75948i 0.0671774i
\(687\) −3.92722 + 13.7832i −0.149833 + 0.525862i
\(688\) 10.4597 + 10.4597i 0.398771 + 0.398771i
\(689\) −38.8515 −1.48012
\(690\) 0 0
\(691\) 18.7943 0.714968 0.357484 0.933919i \(-0.383635\pi\)
0.357484 + 0.933919i \(0.383635\pi\)
\(692\) −2.26427 2.26427i −0.0860745 0.0860745i
\(693\) 1.06275 + 4.53372i 0.0403706 + 0.172222i
\(694\) 35.2932i 1.33971i
\(695\) 0 0
\(696\) −7.15414 + 3.98133i −0.271177 + 0.150912i
\(697\) 5.72810 5.72810i 0.216967 0.216967i
\(698\) −11.5351 + 11.5351i −0.436610 + 0.436610i
\(699\) 27.0597 15.0589i 1.02349 0.569581i
\(700\) 0 0
\(701\) 10.0310i 0.378867i −0.981894 0.189434i \(-0.939335\pi\)
0.981894 0.189434i \(-0.0606652\pi\)
\(702\) 43.1264 39.2266i 1.62770 1.48051i
\(703\) 5.18340 + 5.18340i 0.195496 + 0.195496i
\(704\) −0.201296 −0.00758663
\(705\) 0 0
\(706\) 50.3682 1.89563
\(707\) 8.98258 + 8.98258i 0.337825 + 0.337825i
\(708\) −2.56794 + 9.01260i −0.0965092 + 0.338714i
\(709\) 48.4192i 1.81842i 0.416335 + 0.909211i \(0.363314\pi\)
−0.416335 + 0.909211i \(0.636686\pi\)
\(710\) 0 0
\(711\) −5.68250 + 9.16227i −0.213110 + 0.343612i
\(712\) −1.52596 + 1.52596i −0.0571876 + 0.0571876i
\(713\) −21.8023 + 21.8023i −0.816502 + 0.816502i
\(714\) 4.47177 + 8.03542i 0.167352 + 0.300718i
\(715\) 0 0
\(716\) 13.0602i 0.488083i
\(717\) 43.0197 + 12.2575i 1.60660 + 0.457765i
\(718\) −23.4258 23.4258i −0.874244 0.874244i
\(719\) −10.6931 −0.398786 −0.199393 0.979920i \(-0.563897\pi\)
−0.199393 + 0.979920i \(0.563897\pi\)
\(720\) 0 0
\(721\) −2.07604 −0.0773157
\(722\) 1.58818 + 1.58818i 0.0591060 + 0.0591060i
\(723\) 17.5232 + 4.99284i 0.651693 + 0.185686i
\(724\) 19.2797i 0.716523i
\(725\) 0 0
\(726\) −12.7308 22.8763i −0.472486 0.849020i
\(727\) −30.9245 + 30.9245i −1.14693 + 1.14693i −0.159773 + 0.987154i \(0.551076\pi\)
−0.987154 + 0.159773i \(0.948924\pi\)
\(728\) −7.17345 + 7.17345i −0.265866 + 0.265866i
\(729\) −2.55143 + 26.8792i −0.0944974 + 0.995525i
\(730\) 0 0
\(731\) 8.94354i 0.330789i
\(732\) 1.72503 6.05428i 0.0637590 0.223773i
\(733\) 23.0095 + 23.0095i 0.849876 + 0.849876i 0.990117 0.140241i \(-0.0447879\pi\)
−0.140241 + 0.990117i \(0.544788\pi\)
\(734\) −2.34399 −0.0865184
\(735\) 0 0
\(736\) 29.7782 1.09764
\(737\) 2.65439 + 2.65439i 0.0977759 + 0.0977759i
\(738\) 13.7964 3.23403i 0.507854 0.119046i
\(739\) 31.0959i 1.14388i 0.820295 + 0.571941i \(0.193809\pi\)
−0.820295 + 0.571941i \(0.806191\pi\)
\(740\) 0 0
\(741\) 40.6287 22.6102i 1.49253 0.830606i
\(742\) 7.58042 7.58042i 0.278286 0.278286i
\(743\) −4.41646 + 4.41646i −0.162024 + 0.162024i −0.783463 0.621439i \(-0.786549\pi\)
0.621439 + 0.783463i \(0.286549\pi\)
\(744\) 13.9601 7.76892i 0.511803 0.284822i
\(745\) 0 0
\(746\) 18.4118i 0.674105i
\(747\) 50.4514 11.8263i 1.84592 0.432703i
\(748\) 3.62917 + 3.62917i 0.132695 + 0.132695i
\(749\) 19.1658 0.700305
\(750\) 0 0
\(751\) −20.7634 −0.757668 −0.378834 0.925465i \(-0.623675\pi\)
−0.378834 + 0.925465i \(0.623675\pi\)
\(752\) 0.178885 + 0.178885i 0.00652327 + 0.00652327i
\(753\) 3.29654 11.5697i 0.120132 0.421624i
\(754\) 33.3344i 1.21397i
\(755\) 0 0
\(756\) −0.269328 + 5.68747i −0.00979536 + 0.206851i
\(757\) −27.7515 + 27.7515i −1.00865 + 1.00865i −0.00868333 + 0.999962i \(0.502764\pi\)
−0.999962 + 0.00868333i \(0.997236\pi\)
\(758\) 27.3072 27.3072i 0.991843 0.991843i
\(759\) 6.95274 + 12.4935i 0.252369 + 0.453486i
\(760\) 0 0
\(761\) 51.6155i 1.87106i −0.353246 0.935531i \(-0.614922\pi\)
0.353246 0.935531i \(-0.385078\pi\)
\(762\) 42.1099 + 11.9983i 1.52548 + 0.434652i
\(763\) 3.42351 + 3.42351i 0.123939 + 0.123939i
\(764\) −6.07087 −0.219636
\(765\) 0 0
\(766\) 48.1010 1.73796
\(767\) −22.2631 22.2631i −0.803873 0.803873i
\(768\) −33.0586 9.41932i −1.19290 0.339891i
\(769\) 15.3442i 0.553327i 0.960967 + 0.276663i \(0.0892287\pi\)
−0.960967 + 0.276663i \(0.910771\pi\)
\(770\) 0 0
\(771\) 9.73225 + 17.4881i 0.350498 + 0.629818i
\(772\) −15.2343 + 15.2343i −0.548296 + 0.548296i
\(773\) −16.1229 + 16.1229i −0.579900 + 0.579900i −0.934876 0.354976i \(-0.884489\pi\)
0.354976 + 0.934876i \(0.384489\pi\)
\(774\) −8.24579 + 13.2952i −0.296389 + 0.477887i
\(775\) 0 0
\(776\) 24.7072i 0.886937i
\(777\) 0.826421 2.90046i 0.0296477 0.104053i
\(778\) 38.3147 + 38.3147i